Can anyone out there help me ?

Q1. The lengths of the diagonals of a rhombus are 16 cm and 12 cm respectively.Find the length of each of its sides.

Q2. The sum of two opposite angles of a 11gm is 130 degrees. Find the measure of each of its angles.

Let ABCD is a rhombus and AC and BD are the diagonals that intersect each other at O. AC = 16 cm ; BD = 12 cm

Since diagonals of a rhombus bisect each other at right angle, then

∠ AOD = 90^{0 }and OA = OC = 8 cm ; OB = OD = 6 cm

Now, in Δ AOD ,

AD^{2 }= AO^{2 }+ OD^{2}

^{ }= (8)^{2 }+ (6)^{2 }

= 64 + 36

AD^{2} = 100

AD = 10 cm

So, each side of the rhombus is of 10 cm.

(2)

Let ABCD is a parallelogram.

∠ B + ∠ D = 130^{0 }

∠B + ∠B = 130^{0 }( Opposite angles of parallelogram are equal)

⇒∠B = 65^{0 }= ∠D

Now, ∠B + ∠C = 180^{0 }(Adjacent angles of parallelogram are supplementary

⇒ ∠C = 115^{0}

Now, ∠A = ∠C = 115^{0 }(Opposite angles of parallelogram are equal)

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